I'd be REALLY careful but you need jewlers polish to remove fine scratches from glass. It's basically super super fine sandpaper (something like 4000 grit) along with a polish.
My dad used to bring something like it home from the airport. The maintenance people use it to buff out small scratches in the windows. We used it to buff out tiny scratches in watch faces and the like.
Inquire at a good jeweler, they should know what you need.